Auditory Theory: Acoustics

Lecture 018 Timbre I

Reading Assignment for Lecture 019

Before next lecture please read Sections

5.4 The pipe organ as a timbral synthesiser 226
5.5 Deceiving the ear 228

pages 226 to 247 of Acoustics and Psychoacoustics. We may have a brief quiz on these sections at the beginning of the next class.

Brain Bullets

Timbre

Pitch relates to issues such as notes on a score, key, melody, harmony, tuning systems, and intonation in performance. Loudness relates to matters such as musical dynamic (e.g. pp, p, mp, mf, f, ff, etc.), the balance between members of a musical ensemble (e.g. between individual parts, choir and orchestra, or soloist and accompaniment). Timbre to sound quality descriptions include: mellow, rich, covered, open, dull, bright, dark, strident, grating, harsh, shrill, sonorous, sombre colourless and lacklustre. Timbral descriptors are therefore used to indicate the perceived quality or tonal nature of a sound which can have a particular pitch and loudness also.
The commonly quoted American National Standards Institute formal definition of timbre reflects this: 'Timbre is that attribute of auditory sensation in terms of which a listener can judge two sounds similarly presented and having the same loudness and pitch as being dissimilar'
When considering the notes played on pitched musical instruments, timbre relates to those aspects of the note which can be varied without affecting the pitch, duration or loudness of the note as a whole, such as the spectral components present and the way in which their frequencies and amplitudes vary during the sound.
It is then, convenient to consider a note in terms of three phases: the 'onset' or 'attack' (the build-up from silence at the start of the note), the 'steady state' (the main portion of the note), and the 'offset' or 'release' (the return to silence at the end of the note after the energy source is stopped). The onset and offset portions of a note tend to last for a short time of the order of a few tens of milliseconds (or a few hundredths of a second). Changes that occur during the onset and offset phases, and in particular during the onset, turn out to have a very important role in defining the timbre of a note.
In terms of the timbre of the note, it is not only the variations that occur during the onset and offset that are of interest, but also how they change with time.
'steady state' does not mean that no aspect of the note varies. The timbre of a principal organ stop sounds 'steady' during a prolonged note such as that plotted, which lasts for approximately 2 seconds, but it is clear from the acoustic pressure waveform plot in Figure 5.1 that the amplitude, or 'envelope', varies even during the so-called 'steady-state' portion of this note. This is an important aspect of musical notes to be aware of when, for example, synthesising notes of musical instruments; particularly if using looping techniques on a sampling synthesiser
Psychoacoustics of timbre
that listeners cannot reliably identify musical instruments if the onset and offset phases of notes are removed. For example, if recordings of a note played on a violin open string and the same note played on a trumpet are modified to remove their onset and offset phases in each case, it becomes very difficult to tell them apart.
Thus, for example the initial scraping of the bow on a stringed instrument, the consonant-like onset of a note played on a brass instrument, the breath noise of the flautist, the initial flapping of a reed, the percussive thud of a piano hammer and the final fall of the jacks of a harpsichord back onto the strings are all vital acoustic cues to the timbral identity of an instrument. Careful attention must be paid to such acoustic features, for example when synthesising acoustic musical instruments if the resulting timbre is to sound convincingly natural to listeners.

Critical bands and timbre

The variation in critical bandwidth is such that it becomes wider with increasing frequency, and the general conclusion was drawn in the section on pitch perception in Chapter 3 that no harmonic above about the fifth to seventh is resolved no matter what the value of f0
Harmonics below the fifth to seventh are therefore resolved separately by the hearing system (e.g. see Figure 3.11), which suggests that these harmonics might play a distinct and individual role in timbre perception.
Harmonics above the fifth or seventh, on the other hand, which are not separately isolated by the hearing system are not likely to have such a strong individual effect on timbre perception, but could affect it as groups that lie within a particular critical band.
Instruments amongst those for which spectra have been presented that have significant amplitudes in harmonics above the fifth or seventh during their steady-state phases include organ reed stops, the tenor saxophone, the trumpet , the violin and professional singing voice. The timbres of such instruments might be compared with those of other instruments using descriptive terms such as 'bright', 'brilliant', or 'shrill'. Instruments which do not exhibit energy in harmonics above the fifth or seventh during their steady-state phases include the principal 8', the gedackt 8', the clarinet, oboe and flute, and the trombone, French horn and tuba. In comparison with their counterpart organ stops or other instruments of their category (woodwind or brass), their timbres might be described as being: 'less bright' or 'dark', 'less brilliant' or 'dull', or 'less shrill' or 'bland'.
Within this latter group of instruments there is an additional potential timbral grouping between those instruments which exhibit all harmonics up to the fifth or seventh, such as the clarinet, oboe, flute, compared with those which just have a few low harmonics such as the principal 8', gedackt 8', trombone, French horn and tuba. It may come as a surprise to find the flute in the same group as the oboe and clarinet, but the lack of the seventh harmonic in the flute spectrum compared to the clarinet and oboe is crucial. Notes excluding the seventh harmonic sound considerably less 'reedy' than those with it, the seventh harmonic is one of the lowest which is not resolved by the hearing system (provided the sixth and/or eighth are/is also present). This last point is relevant to the clarinet where the seventh harmonic is present but both the sixth and eighth are weak. The clarinet has a particular timbre of its own due to the dominance of the odd harmonics in its output, and it is often described as being 'nasal'.
Percussion instruments which make use of bars, membranes or plates as their vibrating system which are struck have a distinct timbral quality of their own. This is due to the non-harmonic relationship between the frequencies of their natural modes which provides a clear acoustic cue to their family identity. It gives the characteristic 'clanginess' to this class of instruments which endows them with a timbral quality of their own.

Acoustic cues and timbre perception

Timbre judgements are highly subjective and therefore individualistic. Unlike pitch or loudness judgements, where listeners might be asked to rate sounds on scales of low to high or soft to loud respectively, there is no 'right' answer for timbre judgements.
Grey identified the following acoustic factors with respect to each of the three axes: (1) 'spectral energy distribution' observed as increasing high-frequency components in the spectrum; (2) 'synchronicity in the collective attacks and decays of upper harmonics' from sounds with note onsets in which all harmonics enter in close time alignment to those in which the entry of the harmonics is tapered; and (3) from sounds with 'precedent high-frequency, low-amplitude energy, most often inharmonic energy, during the attack phase' to those without high frequency attack energy.
Variation of some kind is needed during any sound in order to hold the listener's attention. The acoustic communication of new information to a listener, whether speech, music, environmental sounds or warning signals from a natural or person-made source, requires that the input signal varies in some way, with time. Such variation may be of the pitch, loudness or timbre of the sound. The popularity of post-processing effects, particularly chorus (see Chapter 7), either as a feature on synthesisers themselves or as a studio effects unit reflects this. However, whilst these can make sounds more interesting to listen to by time variation imposed by adding post-processing, such an addition rarely does anything to improve the overall naturalness of a synthesised sound.

The pipe organ as a timbral synthesiser

An organ stop which has the same f0 values as on a piano (i.e. 10 for its A4 is 440 Hz) is known as an 'eight foot' (8') rank on the manuals and 'sixteen foot' (16') rank on the pedals, because eight and sixteen feet are the approximate lengths of open pipes of the bottom note of a manual (C2) and the pedals (C1) respectively. A 4' rank and a 2' rank would sound one and two octaves higher than an 8' rank respectively, and a 32' rank would sound one octave lower than a 16' rank. It should be noted that the footage terminology is used to denote the sounding pitch of the rank and give no indication as to whether open or stopped pipes are employed. Thus the bottom pipes of a stopped rank on a manual sounding a pitch equivalent to a rank of 8' open pipes would be four foot long physically but its stop knob would be labelled 8'. Organs have a number of stops on each manual of various footages, most of which are flues. Some are voiced to be used alone as solo stops usually as 8' stops, but the majority are voiced to blend together, allowing variations in loudness and timbre to be achieved by acoustic synthesis involving drawing different combinations of stops. The timbral changes are controlled by reinforcing the natural hamonics of the 8' harmonic series on the manuals (16 foot harmonic series for the pedals).
However, it is important to note that a single 8 foot principal stop, the foundation tone of the organ, produces a sound which is itself rich in harmonics (see Figure 5.1). Therefore the addition of a 4' principal will enhance not only the second harmonic of the 8' stop, but it will also enhance all other even harmonics. The odd harmonics of the 8' pipe are not members of the harmonic series of the 4' pipe. In general, when a stop is added whose to is set to reinforce a member (n = 1, 2, 3, 4, ...) of the natural harmonic series at 8' pitch on the manuals 06' pitch on the pedals), it enhances the (2n, 311, 411, ...) members also. Those stops which reinforce harmonics which are not in unison 0:1) with, or a whole number of octaves (i.e. 2:1,4:1, 8:1, ... 2,,:1) away from the first harmonic are known as 'mutation' stops.
There is a basic pipe organ timbral problem when tuning the instrument to equal temperament (see Chapter 3). Stops have to be tuned in their appropriate integer frequency ratio (see Figure 3.3) to reinforce harmonics appropriately, but as a result of this those which therefore introduce beats when chords are played. For example, supposing two stops are drawn, an 8' and a 2 2/3. The 2 2/3 stop sounds an octave and a third above the 8' stop, and reinforces the third harmonic of the 8' harmonic series and therefore it must be exactly in tune with the third harmonic of the 8' stop. Thus if middle C is played with these two stops drawn, the f0 of the C on the 2 2/3 rank will be exactly in tune with the third harmonic of the C on the 8' rank. If the organ is tuned in equal temperament and the G above middle C is also played to form a two-note chord, the second harmonic of the G on the 8' rank will beat with the to of the C on the 2 2/3 rank as well as with the third harmonic of the C on the 8' rank. Equal-tempered tuning thus colours with beats the desired effect of adding mutation stops to build up the timbre of the organ. Mutation stops therefore tended to go out of fashion with the introduction of equal-tempered tuning on pipe organs (Padgham, 1986). Recent revivals in authentic performance of early music has extended to the pipe organ with the use of non-equal-tempered tuning systems and increased use of mutation stops. This gives new life particularly to contrapuntal music.